In the last years, clinical trials (CTs) have seen an increased uptake of flexible, sequential designs to deliver efficiency or ethical gains [1]}, [2]}. This trend became evident for trials research during the COVID-19 crisis [3]}, [4]}.
Nevertheless, in CTs, the need for ensuring validity with adaptively-collected data [5]}, [6]} has been long recognised and has traditionally dominated over other goals (including regret minimisation).
Applied biostatistics has led the way in developing valid inference methods in a number of adaptive settings, but not for MAB algorithms. For example, the approach of [7]}, which is robust even in case of non-stationarity, shares the rationale in [8]} and [9]}, where a stratified analysis by batches is shown to eliminate bias due to time trends.
